{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Probability Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from prml.rv import (\n",
    "    Bernoulli,\n",
    "    Beta,\n",
    "    Categorical,\n",
    "    Dirichlet,\n",
    "    Gamma,\n",
    "    Gaussian,\n",
    "    MultivariateGaussian,\n",
    "    MultivariateGaussianMixture,\n",
    "    StudentsT,\n",
    "    Uniform\n",
    ")\n",
    "\n",
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 Binary Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bernoulli(\n",
      "    mu=0.75\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "model = Bernoulli()\n",
    "model.fit(np.array([0., 1., 1., 1.]))\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1.1 The beta distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAD8CAYAAABq6S8VAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111b9c978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 1, 100)\n",
    "for i, [a, b] in enumerate([[0.1, 0.1], [1, 1], [2, 3], [8, 4]]):\n",
    "    plt.subplot(2, 2, i + 1)\n",
    "    beta = Beta(a, b)\n",
    "    plt.xlim(0, 1)\n",
    "    plt.ylim(0, 3)\n",
    "    plt.plot(x, beta.pdf(x))\n",
    "    plt.annotate(\"a={}\".format(a), (0.1, 2.5))\n",
    "    plt.annotate(\"b={}\".format(b), (0.1, 2.1))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD8CAYAAAB0IB+mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKaUchAa+Uko5CA18pZRyEBr4SinlIP4/jzp6NSJp/hEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111b9c6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta = Beta(2, 2)\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 2)\n",
    "plt.plot(x, beta.pdf(x))\n",
    "plt.annotate(\"prior\", (0.1, 1.5))\n",
    "\n",
    "model = Bernoulli(mu=beta)\n",
    "model.fit(np.array([1]))\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 2)\n",
    "plt.plot(x, model.mu.pdf(x))\n",
    "plt.annotate(\"posterior\", (0.1, 1.5))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum likelihood estimation\n",
      "10000 out of 10000 is 1\n",
      "Bayesian estimation\n",
      "6649 out of 10000 is 1\n"
     ]
    }
   ],
   "source": [
    "print(\"Maximum likelihood estimation\")\n",
    "model = Bernoulli()\n",
    "model.fit(np.array([1]))\n",
    "print(\"{} out of 10000 is 1\".format(model.draw(10000).sum()))\n",
    "\n",
    "print(\"Bayesian estimation\")\n",
    "model = Bernoulli(mu=Beta(1, 1))\n",
    "model.fit(np.array([1]))\n",
    "print(\"{} out of 10000 is 1\".format(model.draw(10000).sum()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Multinomial Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Categorical(\n",
      "    mu=[ 0.5   0.25  0.25]\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "model = Categorical()\n",
    "model.fit(np.array([[0, 1, 0], [1, 0, 0], [1, 0, 0], [0, 0, 1]]))\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.1 The Dirichlet distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Categorical(\n",
      "    mu=Dirichlet(\n",
      "        alpha=[ 1.  1.  1.]\n",
      "    )\n",
      ")\n",
      "Categorical(\n",
      "    mu=Dirichlet(\n",
      "        alpha=[ 3.  2.  1.]\n",
      "    )\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "mu = Dirichlet(alpha=np.ones(3))\n",
    "model = Categorical(mu=mu)\n",
    "print(model)\n",
    "\n",
    "model.fit(np.array([[1., 0., 0.], [1., 0., 0.], [0., 1., 0.]]))\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 The Gaussian Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlEAAAEzCAYAAAARqFYSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFABAByUKAKCDEgUA0EGJAgDo8H8QkDDuTviskwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111f57dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "uniform = Uniform(low=0, high=1)\n",
    "plt.figure(figsize=(10, 5))\n",
    "\n",
    "plt.subplot(1, 3, 1)\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 5)\n",
    "plt.annotate(\"N=1\", (0.1, 4.5))\n",
    "plt.hist(uniform.draw(100000), bins=20, normed=True)\n",
    "\n",
    "plt.subplot(1, 3, 2)\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 5)\n",
    "plt.annotate(\"N=2\", (0.1, 4.5))\n",
    "plt.hist(0.5 * (uniform.draw(100000) + uniform.draw(100000)), bins=20, normed=True)\n",
    "\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 5)\n",
    "sample = 0\n",
    "for _ in range(10):\n",
    "    sample = sample + uniform.draw(100000)\n",
    "plt.annotate(\"N=10\", (0.1, 4.5))\n",
    "plt.hist(sample * 0.1, bins=20, normed=True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3.4 Maximum Likelihood for the Gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MultivariateGaussian(\n",
      "    mu=[ 0.91852581  1.17919155]\n",
      "    cov=[[ 4.29224408  0.1551223 ]\n",
      " [ 0.1551223   3.58170912]]\n",
      ")\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAD8CAYAAABgmUMCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111ff1e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.random.normal(loc=1., scale=2., size=(100, 2))\n",
    "gaussian = MultivariateGaussian()\n",
    "gaussian.fit(X)\n",
    "print(gaussian)\n",
    "\n",
    "x, y = np.meshgrid(\n",
    "    np.linspace(-10, 10, 100), np.linspace(-10, 10, 100))\n",
    "p = gaussian.pdf(\n",
    "    np.array([x, y]).reshape(2, -1).T).reshape(100, 100)\n",
    "plt.scatter(X[:, 0], X[:, 1], facecolor=\"none\", edgecolor=\"steelblue\")\n",
    "plt.contour(x, y, p)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3.6 Bayesian inference for the Gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112670a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = Gaussian(0, 0.1)\n",
    "model = Gaussian(mu, 0.1)\n",
    "\n",
    "x = np.linspace(-1, 1, 100)\n",
    "plt.plot(x, model.mu.pdf(x), label=\"N=0\")\n",
    "\n",
    "model.fit(np.random.normal(loc=0.8, scale=0.1, size=1))\n",
    "plt.plot(x, model.mu.pdf(x), label=\"N=1\")\n",
    "\n",
    "model.fit(np.random.normal(loc=0.8, scale=0.1, size=1))\n",
    "plt.plot(x, model.mu.pdf(x), label=\"N=2\")\n",
    "\n",
    "model.fit(np.random.normal(loc=0.8, scale=0.1, size=8))\n",
    "plt.plot(x, model.mu.pdf(x), label=\"N=10\")\n",
    "\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(0, 5)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD8CAYAAAB0IB+mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1127b8978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 2, 100)\n",
    "for i, [a, b] in enumerate([[0.1, 0.1], [1, 1], [2, 3], [4, 6]]):\n",
    "    plt.subplot(2, 2, i + 1)\n",
    "    gamma = Gamma(a, b)\n",
    "    plt.xlim(0, 2)\n",
    "    plt.ylim(0, 2)\n",
    "    plt.plot(x, gamma.pdf(x))\n",
    "    plt.annotate(\"a={}\".format(a), (1, 1.6))\n",
    "    plt.annotate(\"b={}\".format(b), (1, 1.3))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gaussian(\n",
      "    mu=0\n",
      "    tau=Gamma(\n",
      "        a=1\n",
      "        b=1\n",
      "    )\n",
      "    var=None\n",
      ")\n",
      "Gaussian(\n",
      "    mu=0\n",
      "    tau=Gamma(\n",
      "        a=51.0\n",
      "        b=94.73272357871433\n",
      "    )\n",
      "    var=None\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "tau = Gamma(a=1, b=1)\n",
    "model = Gaussian(mu=0, tau=tau)\n",
    "print(model)\n",
    "\n",
    "model.fit(np.random.normal(scale=1.414, size=100))\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 2.3.7 Student's t-distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gaussian(\n",
      "    mu=2.2695020512383577\n",
      "    var=46.95748684941486\n",
      "    tau=0.02129585859666723\n",
      ")\n",
      "StudentsT(\n",
      "    mu=-0.19463421094478062\n",
      "    tau=1.4665461746068318\n",
      "    dof=0.9028354354811661\n",
      ")\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nV0qpCKThrpRSEej/A9VRvgmc7gT6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1120ab438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.random.normal(size=20)\n",
    "X = np.concatenate([X, np.random.normal(loc=20., size=3)])\n",
    "plt.hist(X.ravel(), bins=50, normed=1., label=\"samples\")\n",
    "\n",
    "students_t = StudentsT()\n",
    "gaussian = Gaussian()\n",
    "\n",
    "gaussian.fit(X)\n",
    "students_t.fit(X)\n",
    "\n",
    "print(gaussian)\n",
    "print(students_t)\n",
    "\n",
    "x = np.linspace(-5, 25, 1000)\n",
    "plt.plot(x, students_t.pdf(x), label=\"student's t\", linewidth=2)\n",
    "plt.plot(x, gaussian.pdf(x), label=\"gaussian\", linewidth=2)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 2.3.9 Mixture of Gaussians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MultivariateGaussianMixture(\n",
      "    mu=[[ 5.06087392 -5.07813706]\n",
      " [-4.9724865  -5.09928156]\n",
      " [-0.05584106  4.99523381]]\n",
      "    cov=[[[ 1.11567912 -0.01717074]\n",
      "  [-0.01717074  1.04457722]]\n",
      "\n",
      " [[ 0.89251355 -0.0138146 ]\n",
      "  [-0.0138146   1.07986159]]\n",
      "\n",
      " [[ 0.81797404  0.03778106]\n",
      "  [ 0.03778106  0.93690783]]]\n",
      "    coef=[ 0.33333333  0.33333333  0.33333333]\n",
      ")\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAD8CAYAAABgmUMCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b88e0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = np.random.normal(size=(100, 2))\n",
    "x1 += np.array([-5, -5])\n",
    "x2 = np.random.normal(size=(100, 2))\n",
    "x2 += np.array([5, -5])\n",
    "x3 = np.random.normal(size=(100, 2))\n",
    "x3 += np.array([0, 5])\n",
    "X = np.vstack((x1, x2, x3))\n",
    "\n",
    "model = MultivariateGaussianMixture(n_components=3)\n",
    "model.fit(X)\n",
    "print(model)\n",
    "\n",
    "x_test, y_test = np.meshgrid(np.linspace(-10, 10, 100), np.linspace(-10, 10, 100))\n",
    "X_test = np.array([x_test, y_test]).reshape(2, -1).transpose()\n",
    "probs = model.pdf(X_test)\n",
    "Probs = probs.reshape(100, 100)\n",
    "plt.scatter(X[:, 0], X[:, 1])\n",
    "plt.contour(x_test, y_test, Probs)\n",
    "plt.xlim(-10, 10)\n",
    "plt.ylim(-10, 10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
